The current counterweight exercise machine has a frame for supporting a plurality of weights. The user assembles a predetermined number of weights for training the hands or legs of the user in vertical direction. Users can train his (or her muscle) by applying a force to balance the weight of the weights. In some improve designs, some sub-weights are used with the main weights to cause that the user can assemble some weights to have a desire weight. However the sub-weights are directly added to the main weights, it is inconvenient as the user detaches the sub-weights from the main weights.